Firstly, if you have been married more than once, you only need evidence of the end of the most recent marriage to prove eligibility for a new marriage, which is quite separate to providing a paper trail for name changes and proving identity.
To answer this question, I refer directly from the Guidelines for Marriage Celebrants: 4.5.1 Evidence Of Death Of Former Spouse
In the case of a party whose last marriage ended with the death of their spouse, couples must be advised the marriage cannot take place until evidence of the death has been provided.
The evidence of the termination of that marriage will be the spouse’s original death certificate.
Died In Australia
If the party wishing to marry does not have the death certificate, and their spouse died in Australia, the party should be able to obtain the death certificate from the Registry of Births, Deaths & Marriages (BDM) in the State or Territory where their spouse died.
Spouse Died Overseas
If a party’s former spouse died overseas, the authorised celebrant should still sight an original death certificate.
If an original death certificate is not available the authorised celebrant should contact the Attorney General’s Department for guidance.
Death Certificate In Another Language
If the party gives the authorised celebrant a death certificate in a language other than English, they also need to provide a translation of the death certificate by a NAATI accredited translator (see Part 4.10 of these Guidelines).
A translation by the party, a relative or a friend is not sufficient.
Uncertainty of the identity
If an authorised celebrant is not certain of the identity of a deceased person, they should insist on the production of a certificate that shows particulars of the previous marriage to the now deceased person, as well as evidence of the person’s death.
Statutory declarations are not acceptable evidence of the death of a person’s former spouse.